Statistical mechanics of time series. (arXiv:1907.04925v1 [q-fin.ST])

Thu, 11 Jul 2019 23:01:51 GMT

Countless natural and social multivariate systems are studied through sets of
simultaneous and time-spaced measurements of the observables that drive their
dynamics, i.e., through sets of time series. Typically, this is done via
hypothesis testing: the statistical properties of the empirical time series are
tested against those expected under a suitable null hypothesis. This is a very
challenging task in complex interacting systems, where statistical stability is
often poor due to lack of stationarity and ergodicity. Here, we describe an
unsupervised, data-driven framework to perform hypothesis testing in such
situations. This consists of a statistical mechanical theory - derived from
first principles - for ensembles of time series designed to preserve, on
average, some of the statistical properties observed on an empirical set of
time series. We showcase its possible applications on a set of stock market
returns from the NYSE.